geometric quantization higher geometric quantization
geometry of physics: Lagrangians and Action functionals + Geometric Quantization
prequantum circle n-bundle = extended Lagrangian
prequantum 1-bundle = prequantum circle bundle, regularcontact manifold,prequantum line bundle = lift of symplectic form to differential cohomology
…coherent state in geometric quantization…
The original reference that interpreted coherent states in geometric quantization over Kähler manifolds is
A review and further developments of these considerations are in
Generalization to non-Kähler symplectic manifolds is in
See also
Anatol Odzijewicz, Coherent state method in geometric quantization, in Twenty Years of Bialowiez: a mathematical anthology, Aspects of Differential Geometric Methods in Physics_ (pp 47-78) , World Sci. Monogr. Ser. Math. 8 (2005); Coherent states and geometric quantization, Comm. Math. Phys. 150 (1992), no. 2, 385–413 doi 94c:58077
Brian Charles Hall, Geometric quantization and the generalized Segal–Bargmann transform for Lie groups of compact type, Comm. Math. Phys., 226:233–268, 2002. doi
D. J. Rowe, Coherent states, induced representations, geometric quantization, and their vector coherent state extensions, Symmetry in physics, 177–188, CRM Proc. Lecture Notes 34, Amer. Math. Soc. 2004. MR2005a:81100
C. Florentino, P. Matias, J. Mourão, J. P. Nunes, Geometric quantization, complex structures and the coherent state transform, J. Funct. Anal. 221(2):303–322, 2005 MR2005m:53179 doi